Theorems · Theorem · commutative algebra
IsSMulRegular.of_flat_of_isBaseChange
∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [Module.Flat R S] [inst_4 : AddCommMonoid M] [inst_5 : Module R M] [inst_6 : AddCommMonoid N]
[inst_7 : Module R N] [inst_8 : Module S N] [inst_9 : IsScalarTower R S N] {f : M →ₗ[R] N},
IsBaseChange S f → ∀ {x : R}, IsSMulRegular M x → IsSMulRegular N ((algebraMap R S) x)- Defined in
- Mathlib.RingTheory.Flat.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- LinearMap.idproof · cited by 625
- Module.Flatstatement and proof · cited by 279
Cited by3
Results whose statement or proof uses this declaration.
- RingTheory.Sequence.IsWeaklyRegular.of_flat_of_isBaseChangeproof · cited by 3
- IsSMulRegular.of_isLocalizedModuleproof · cited by 1
- IsSMulRegular.of_flatproof · cited by 0